pradeep sharma department of mechanical engineering (joint) department of physics university of...
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Pradeep Sharma
Department of Mechanical Engineering
(Joint) Department of Physics
University of Houston
Electromechanical Coupling in Hard Materials: Energy Scavenging and
Storage
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What is piezoelectricity? What is flexoelectricity? Nanoscale effects….
Introduction
Materials design
Size-effects
Possibility of piezoelectric materials without piezoelectric materials ! Enhanced piezoelectricity in nanostructures….
Indentation experiments and theory
Energy harvesting and storage
Enhancements at the nanoscale, the origins of the dead-layer effect in nanocapacitors
Overview
New international collaboration models
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What is piezoelectricity?
Coupling between electrical and mechanical behavior of a material
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Applications
• Consumer items like lighters…shoes….tennis rackets…
• Powering soldiers…. harvesting energy from pedestrians….sonars
• Atomic force microscopy; precise control over mechanical motion
• Robotic arms and artificial muscles
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-
--
-
+
++
+
+
Polarization = 0
C
-
--
-
+
++
+
+
Force
C
Undeformed State
Force
Deformed State
Center of positive and negative charges coincide in the undeformed state. Plus, the centroid is a center of symmetry.
Absence of piezoelectricity---centrosymmetric crystals*
*This cartoon is at odds with the modern theory of polarization based on the Berry-phase concept. Nevertheless, it is used here for ease of illustration
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A uniform strain causes polarization and vice-versa
i ijk jkP d
Odd order tensor cannot be sustained by centrosymmetric
crystal—hence piezoelectricity is restricted to non-
centrosymmetric crystals
-
-
++
+
.C
-
-
++
+
.C+
--
++
- -
-
+
+
- PP
A
B
A
B
Working definition of piezoelectricity
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0,
jki ijk jk ijkl
lfor non piezo materials
P dx
Cl-
Na+
Cl-
Cl-
Cl- -P
Center of negative charge
Cl-
Na+
Cl-
Cl-
Cl- -P
Center of negative charge
Cl-
Na+
Cl-
Cl-
Cl- -
Cl-
Na+
Cl-
Cl-
Cl- -
Na+
Cl-
Cl-
Cl- --P
Center of negative charge
In principle, flexoelectric coefficients are non-zero for all dielectrics (although may be negligibly small in some
cases)—experimentally verified for many materials!
Beyond uniform strain and polarization----flexoelectricity
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Cross L. Eric, Journal of Materials Science, 41, 53-63, 2006
10NaCl
6BST
6PMN
6PZT
2.84 10
100 10
5 10
2 10
C
m
C
m
C
m
C
m
9Graphene 1.128 10
C
m
Cross and co-workers: The magnitude of the flexoelectric
coefficient is of the order of 10-6 C/m which is much larger than the generally accepted lower bound of (10-9 – 10-11 C/m).
Graphene, BaTiO3 and others (non-ferroelectric state)
Dumitrica et. al., 2002
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Direction of Strain Gradient
Apparent piezoelectric behavior at nanoscale without using piezoelectric materials
a~x a
Uniform Stress
*Cross and co-workers; N. Sharma, R. Maranganti and P. Sharma, J. Mech. Phy. Solids, 2007
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High elastic and dielectric contrast
Small size
Non-centrosymmetric shape
Optimum volume fraction
Apparent piezoelectric behavior at nanoscale without using piezoelectric materials
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Ensure that the defective structure is dielectric through electronic structure calculations
Coaxing Graphene to be piezoelectric
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0.398 C/m2
Coaxing Graphene to be piezoelectric
Roughly 50 % of ZnO and 110 % of Boron Nitride Nanotubes
Circular holes
• Thinnest piezoelectric material---energy harvesting for stretchable electronics, nearly invisible sensors, artificial muscles
• Bio-compatible membranes for artificial ears
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Volume fraction10
Average polarization
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%
Hole Size = 3nm
σxxσxx
Theoretical calculations for BTO
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A
B
AAC
A
A
B
B
C
Manufacturable Superlattices
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• Experiments indicate that flexoelectric coefficients can be almost 1000 - 10,000 time larger in ferroelectrics compared to ordinary dielectrics
• This suggests the possibility of an additive effect• Conversely, possible to design structures that
eliminate existing piezoelectricity or tailor it as needed
• Need further physical insights from both theory and atomistics….complications---anisotropy, potentials
Intrinsically piezoelectric materials
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Theoretical and atomistic analysis of a paradigmatical nanostructure: cantilever
beam
2eff fd d k
h
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Atomistic Study of BaTiO3 in cubic and tetragonal phase
• Conventional (core-shell) potentials are inadequate…..use fixed charges, cannot re-adjust to match changing electrostatic environment…
• We employed a quantum mechanically derived polarizable force field for BaTiO3 (--currently development is in progress for SrTiO3).
• Core has a Gaussian distributed fixed charge while the shell has Gaussian distributed variable charge dynamically updated by self-consistent charge equilibration method
• Shell charges can move w.r.t core, transfer to shells of other atoms; accurate description of polarization
• Non-bonded terms (Pauli repulsion, Van der Waals forces) are accounted for via 3-term Morse potential
• Inputs obtained entirely from first principles calculations and validated against experimental data
• Well tested……• Drawback: custom code; non-parallelized; while
much faster than first principles, system size is restricted to roughly 1000 atoms (self-consistent charge equilibration is quite expensive)
Sharma group----University of Houston, Tahir Cagin---Texas A&M, student from Tunisia
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BaTiO3 both phases: Enhanced “apparent” piezoelectricity..
* M. Majdoub , P. Sharma, T. Cagin, Phy. Rev., 2008 * M. Majdoub , P. Sharma, T. Cagin, Phy. Rev., Erratum, 2009
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Energy Harvesting
• Piezoelectric nanostructures can dramatically enhance energy harvesting*
• For PbTiO3 cantilever beams, our results indicate that the total harvested power peak value can increase by 100% at the nano-size (under short circuit conditions) and nearly a 200% increase may be achieved for specifically tailored cross-section shapes.
* M. Majdoub , P. Sharma, T. Cagin, Phy. Rev., 2008
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Energy HarvestingJemai, Najar, Chafra---Tunisia, Ounaies---Penn State
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Energy HarvestingJemai, Najar, Chafra---Tunisia, Ounaies---Penn State
Energy Harvesting System
Homogenized AFC patch
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Simulation of the harvested electrical power
• Investigation of the energy harvester dynamic behavior of the beam with AFC patch: Harvested power, voltage and current.
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Speculation: Indentation size effect?
In principle, the flexoelectric size-effect should be observable in indentation experiments.
Sharma group—University of Houston, Sami El-Borgi--Tunisia
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Theoretical Results: A regular piezoelectric material
2 01 22 aCaC wP
1 1
2 2/
P as C s a C
w
[Karapetian, Kachanov, Kalinin and co-workers]
Purely mechanical loading on an anisotropic
piezoelectric material
For example, in the isotropic purely elastic half-space case
(Oliver, Pharr)1 rC E
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Theoretical results: Effect of flexoelectricity on indentation
132 2
size effec
Aa
t
Ce Aa
P a
as C
w
We derived analytical solution of the indentation problem incorporating anisotropy,
piezoelectricity and flexoelectricity----the solution fills 14 pages!
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Theoretical results: Effect of flexoelectricity on indentation
132
/22
/
size effect
AaCP
s a a e aw
ACa
We derived analytical solution of the indentation problem incorporating anisotropy,
piezoelectricity and flexoelectricity----the solution fills 14 pages!
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Load Application (Coil & Magnet)
Support Springs
Displacement Sensor(Capacitance Gauge)
IndenterSample
Motorized Stage
Berkovich indent on BTO surfaceLoad: 8mN; Depth into surface: 200nm
Nanoindentation - Schematic
In parallel, we conducted experiments with varying indentation size…..single crystal BaTiO3
Indentation experiments (collaboration with Ken White)
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Contact stiffness vs contact radius for
BaTiO3
• Indentation experiments indicate a large size effect (see the star-data points). For example, compared to the size-independent behavior (red line), around 10 nm, there is a doubling of contact stiffness.
• Incorporation of flexoelectricity correctly captures the size-effect
• Another possible source of size-effect dislocation activity---role of domains unlikely
1
2/s a C
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Contact stiffness vs contact radius for
Quartz
• No size-effect is observed for Quartz!
• This observation strengthens our argument that flexoelectricity is the cause of indentation size-effect since Quartz has very small flexoelectricity constants (in contrast to BaTiO3) while the dislocation nucleation behavior between the two is not expected to be dramatically different.
1
2/s a C
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Nanocapacitors
Energy storage
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Nanocapacitors
Cd
V2
V1
V2 - V1
V(x)
+++++
-----
Energy storageMiniaturization of
electronics
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Take 2.7 nm SrTiO3 capacitor……
We can expect a capacitance of 1600 fF/m-2
Reality? ----258 fF/m-2 !!
The reason is ascribed to the so-called dead-layer effect
Mechanism?---growth induced defects, incomplete electrode screening, strain, grain boundaries, poor interface…..
1 1 1 1
eff i o iC C C C
The dead-layer bottleneck
Stengel and Spaldin, Nature Materials, 2006
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The first, “first principles” calculations clarifying the dead-layer mechanism: Stengel and Spaldin (Nature, 2006; Physical Review B,
2005); Rabe (Nature Nanotechnology, 2006)
State of the art--ab initio calculations [Stengel-Spaldin, 2006]
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Electric field penetration in real metals triggers a secondary mechanism--flexoelectricity
• Even though flexoelectricity will not occur without apriori presence of field penetration; it becomes quite important
• Why is this “hair-splitting” important?
What is the real cause of the dead-layer?
M. S. Majdoub, R. Maranganti, and P. Sharma, Physical Review B, 2009
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• New graduate degree models: Tunisian M.S. student is co-advised by collaborator from
Tunisia and faculty from University of Houston. The student spends 4-8 months in the US and
the remainder part of the time Tunisia.
• The student defends his/her M.S. thesis in Tunisia. All PI’s jointly publish the results
• The student returns to US to pursue PhD
• Two students have successfully gone through this and are now pursuing their PhD at
University of Houston.
• Four more students are expected to join UH in February/March.
a) b) c)
d)
e)) f)
g)
International Joint Collaborative Program
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Participants
• Pradeep Sharma (University of Houston, USA)
• Tahir Cagin (Texas A&M University, USA)
• Zoubeida Ounaies (Penn State, USA)
• Sami El-Borgi (EPT, Tunisia)
• Fehmi Najar (EPT, Tunisia)
• Moez Chafra (EPT, Tunisia)
• Bin Zineb Tarak (Universite de Lorraine, France)
• Students: Mohamed Sabri Madoub, Mohamed
Gharbi, Nikhil Sharma, Raouf Mbarki, Swapnil
Chandratre